CH 224 |
Group Theory |
3-0-0-6 |
Syllabus: Definitions and Theorems of Group Theory:
Properties of Group and examples, Subgroups, Classes. Molecular Symmetry and
the Symmetry Groups: Symmetry elements and Operations: symmetry planes and reflections,
the inversion Center, Proper Axes and proper
rotation, and Improper axes and improper rotations. Products of symmetry
Operations. Equivalent symmetry elements and equivalent Atoms. General
relations among symmetry elements and Operations. Symmetry Elements and
Optical Isomerism. The symmetry point groups. Symmetries with multiple High-
Order Axes. Classes of symmetry Operations. A systematic Procedure for
symmetry Classification of molecules. Representations of Groups: Comments on
Matrices and Vectors. Representation of groups. The "Great Orthogonality
Theorem" and its
consequences. Character Tables. Representation for Cyclic Groups. Group
Theory and Quantum Mechanics: Wave function as bases for irreducible
representations. The Direct Product. Detection of non-zero integrals.
Symmetry Adapted Linear Combinations: Derivation of Projection Operators. Use
of Projection Operators to construct SALCs. Molecular Orbital Theory and its
Application in Organic Chemistry: General Remarks. Symmetry factoring of
secular equations. Carbocyclic system. More general cases of LCAO-MO bonding.
Naphthalene. Electronic excitations of Naphthalene:selection rules and configuration interaction.
Three center Bonding. Symmetry based selection
rules for cyclization reactions. Molecular Orbital Theory for Inorganic and
Organometallic Compounds: Transformation Properties of Atomic Orbitals.
Molecular orbitals for bonding in ABn molecules:
The Tetrahedral AB4 cases. Molecular orbitals for bonding in ABn molecules. Text
Book 1. F. A. Cotton, Chemical Applications of Group
Theory, 3rd Ed, John Wiley & Sons, 1990. Reference: 1. Molecular Symmetry and Group Theory: "A Programmed Introduction to Chemical
Applications" by Alan
Vincent; 2nd Edition, Wiley. |